Set the oven to 425 degrees Fahrenheit. Poke whole sweet potatoes with a fork, creating a few holes through which steam can escape, then place sweet potatoes on a baking sheet. Bake for about 45 minutes. Remove from the oven. Once they’re no longer piping hot, slice into 1-inch chunks. Set aside.
In a saucepan, combine the heavy cream, milk, sweet potatoes, cinnamon, nutmeg, allspice, and salt and bring to a boil. Remove from heat and set aside.
In a separate bowl, whisk egg yolks and sugar together until light and creamy.
Whisk the sugar-and-yolk mixture into the warm dairy mixture, working very slowly so as not to cook the eggs. Once combined, use an immersion blender to puree mixture until the potatoes are smooth. Set aside or place in refrigerator to cool.
Set the oven to 300 degrees Fahrenheit. Once the mixture is no longer warm, pour it into a large, shallow ramekin and set in the middle of an ovenproof pan. Prepare a water bath: pour enough water into the pan to reach at least halfway up the sides of the ramekin. Bake at 300 degrees for 20 to 30 minutes, until custard is set, then remove from the oven and place in refrigerator until cool.
Lastly, the fun part: add a thin layer of granulated sugar and torch to a golden-brown.